x NOTATION Zp set of p-adic integers: 12.9, Problem 4 Tp /7-adic solenoid: 12.9, Problem 4 G/H, H\G homogeneous space of left (right) cosets of a subgroup H in a group G: 12.10 and 12.11 G • A union of the orbits of the points of a subset A of E, with respect to an action of G on E: 12.10 E/G space of orbits with respect to G: 12.10 ^C(X) space of continuous complex-valued functions on X: 12.14 E/F quotient normed space of a normed space E by a vector subspace F: 12.14 (x, x'y, <#', jc> x'(x) for a vector x € E and a continuous linear form x' e E' (the dual of E): 12.15 *u transpose of a continuous linear map- ping: 12.15 U(E) unitary group of a Hilbert space E : 12. 1 5, Problem 8 «^*(X; K), «Pfc(X; K) space of continuous complex- valued functions with support contained in the compact subset K of X: 13.1 Jf (X), JTC(X) space of continuous complex-valued functions on X with compact support: 13.1 sx Dirac measure at the point x: 13.1 g • \i measure with density g with respect to /i : 13.1 and 13.13 n(p) image of a measure JJL under a proper con- tinuous mapping n: 13.1 and 13.1, Problem 8 A*u > fl I U measure induced on an open set U by a measure \JL (or restriction of $ to U): 13.1 MC(X), M(X) space of complex measures on X: 13.1 J/4<, J/(*) 44X) integral of/eJf(X) with respect to /*: 13.1 Jf R(X; K) space of continuous real-valued functions with support contained in the compact subset K of X: 13.2